A dichotomy theorem for mono-unary algebras
We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.
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Su Gao (2000)
Fundamenta Mathematicae
We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.
Bordalo, G. (1989)
Portugaliae mathematica
Ivan Chajda, Helmut Länger (2002)
Czechoslovak Mathematical Journal
A variety is called normal if no laws of the form are valid in it where is a variable and is not a variable. Let denote the lattice of all varieties of monounary algebras and let be a non-trivial non-normal element of . Then is of the form with some . It is shown that the smallest normal variety containing is contained in for every where denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of consisting of all normal elements of...
Bohdan Zelinka (2003)
Mathematica Bohemica
Let be an infinite locally finite tree. We say that has exactly one end, if in any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considered and investigated with the aim of showing, whether they give algebras with the required properties. At...
Danica Jakubíková-Studenovská (1998)
Czechoslovak Mathematical Journal
Bohdan Zelinka (1996)
Mathematica Bohemica
A tolerance on an algebra is defined similarly to a congruence, only the requirement of transitivity is omitted. The paper studies a special type of tolerance, namely atomary tolerances. They exist on every finite algebra.
Jaroslav Ježek, Tomáš Kepka (1996)
Acta Universitatis Carolinae. Mathematica et Physica
Jiří Novotný (1986)
Časopis pro pěstování matematiky
Anna Kartashova (2001)
Discussiones Mathematicae - General Algebra and Applications
In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.
Danica Jakubíková-Studenovská, Jozef Pócs (2008)
Czechoslovak Mathematical Journal
For an uncountable monounary algebra with cardinality it is proved that has exactly retracts. The case when is countable is also dealt with.
J. Chvalina (1987)
Matematički Vesnik
Jan Chvalina (1978)
Archivum Mathematicum
Jan Chvalina (1978)
Archivum Mathematicum
Jana Ryšlinková (1987)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Steve Seif (2013)
Commentationes Mathematicae Universitatis Carolinae
An M-Set is a unary algebra whose set of operations is a monoid of transformations of ; is a G-Set if is a group. A lattice is said to be represented by an M-Set if the congruence lattice of is isomorphic to . Given an algebraic lattice , an invariant is introduced here. provides substantial information about properties common to all representations of by intransitive G-Sets. is a sublattice of (possibly isomorphic to the trivial lattice), a -product lattice. A -product...
Miroslav Novotný (1996)
Czechoslovak Mathematical Journal
Miroslav Novotný (1996)
Czechoslovak Mathematical Journal
Miroslav Novotný (1991)
Czechoslovak Mathematical Journal
Danica Jakubíková-Studenovská (1995)
Czechoslovak Mathematical Journal
Danica Jakubíková-Studenovská (1988)
Czechoslovak Mathematical Journal
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